Geodesic
On the solutions of quadratic Diophantine equations
Documenta mathematica, Tome 15 (2010), pp. 347-385
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We determine a finite set of representatives of the set of local solutions in a maximal lattice modulo the stabilizer of the lattice in question for a quadratic Diophantine equation. Our study is based on the works of Shimura on quadratic forms, especially citeSh3 and citeSh4. Indeed, as an application of the result, we present a criterion (in both global and local cases) of the maximality of the lattice of (11.6a) in citeSh3. This gives an answer to the question (11.6a). As one more global application, we investigate primitive solutions contained in a maximal lattice for the sums of squares on each vector space of dimension 4,6,8, or 10 over the field of rational numbers.
DOI : 10.4171/dm/300
Classification : 11D09, 11E08, 11E12
Mots-clés : maximal lattices, quadratic Diophantine equations 
@article{10_4171_dm_300,
     author = {Takashi Yoshinaga},
     title = {On the solutions of quadratic {Diophantine} equations},
     journal = {Documenta mathematica},
     pages = {347--385},
     year = {2010},
     volume = {15},
     doi = {10.4171/dm/300},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/300/}
}
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Takashi Yoshinaga. On the solutions of quadratic Diophantine equations. Documenta mathematica, Tome 15 (2010), pp. 347-385. doi: 10.4171/dm/300

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